Search for lepton-flavor-violating decays
D
0→ X
0e
μ
∓J. P. Lees,1V. Poireau,1V. Tisserand,1E. Grauges,2A. Palano,3G. Eigen,4D. N. Brown,5Yu. G. Kolomensky,5M. Fritsch,6 H. Koch,6 T. Schroeder,6 R. Cheaib,7bC. Hearty,7a,7b T. S. Mattison,7bJ. A. McKenna,7bR. Y. So,7bV. E. Blinov,8a,8b,8c A. R. Buzykaev,8aV. P. Druzhinin,8a,8bV. B. Golubev,8a,8bE. A. Kozyrev,8a,8bE. A. Kravchenko,8a,8bA. P. Onuchin,8a,8b,8c S. I. Serednyakov,8a,8bYu. I. Skovpen,8a,8bE. P. Solodov,8a,8bK. Yu. Todyshev,8a,8bA. J. Lankford,9B. Dey,10J. W. Gary,10
O. Long,10A. M. Eisner,11W. S. Lockman,11W. Panduro Vazquez,11 D. S. Chao,12C. H. Cheng,12B. Echenard,12 K. T. Flood,12D. G. Hitlin,12J. Kim,12Y. Li,12D. X. Lin,12T. S. Miyashita,12 P. Ongmongkolkul,12J. Oyang,12 F. C. Porter,12M. Röhrken,12Z. Huard,13B. T. Meadows,13B. G. Pushpawela,13M. D. Sokoloff,13L. Sun,13,*J. G. Smith,14
S. R. Wagner,14D. Bernard,15M. Verderi,15D. Bettoni,16a C. Bozzi,16a R. Calabrese,16a,16b G. Cibinetto,16a,16b E. Fioravanti,16a,16bI. Garzia,16a,16bE. Luppi,16a,16b V. Santoro,16a A. Calcaterra,17R. de Sangro,17 G. Finocchiaro,17 S. Martellotti,17P. Patteri,17I. M. Peruzzi,17M. Piccolo,17 M. Rotondo,17A. Zallo,17 S. Passaggio,18C. Patrignani,18,† B. J. Shuve,19H. M. Lacker,20B. Bhuyan,21U. Mallik,22C. Chen,23J. Cochran,23S. Prell,23A. V. Gritsan,24N. Arnaud,25
M. Davier,25F. Le Diberder,25A. M. Lutz,25G. Wormser,25D. J. Lange,26D. M. Wright,26J. P. Coleman,27 E. Gabathuler,27,‡D. E. Hutchcroft,27D. J. Payne,27C. Touramanis,27A. J. Bevan,28F. Di Lodovico,28,§R. Sacco,28 G. Cowan,29 Sw. Banerjee,30D. N. Brown,30C. L. Davis,30A. G. Denig,31W. Gradl,31K. Griessinger,31A. Hafner,31
K. R. Schubert,31R. J. Barlow,32,∥ G. D. Lafferty,32R. Cenci,33A. Jawahery,33D. A. Roberts,33 R. Cowan,34 S. H. Robertson,35a,35bR. M. Seddon,35b N. Neri,36a F. Palombo,36a,36bL. Cremaldi,37R. Godang,37,¶ D. J. Summers,37 P. Taras,38G. De Nardo,39C. Sciacca,39G. Raven,40C. P. Jessop,41J. M. LoSecco,41K. Honscheid,42R. Kass,42A. Gaz,43a
M. Margoni,43a,43bM. Posocco,43a G. Simi,43a,43bF. Simonetto,43a,43bR. Stroili,43a,43bS. Akar,44E. Ben-Haim,44 M. Bomben,44G. R. Bonneaud,44G. Calderini,44J. Chauveau,44G. Marchiori,44J. Ocariz,44M. Biasini,45a,45bE. Manoni,45a A. Rossi,45aG. Batignani,46a,46bS. Bettarini,46a,46bM. Carpinelli,46a,46b,**G. Casarosa,46a,46bM. Chrzaszcz,46aF. Forti,46a,46b
M. A. Giorgi,46a,46bA. Lusiani,46a,46cB. Oberhof,46a,46b E. Paoloni,46a,46bM. Rama,46a G. Rizzo,46a,46bJ. J. Walsh,46a L. Zani,46a,46bA. J. S. Smith,47F. Anulli,48aR. Faccini,48a,48bF. Ferrarotto,48aF. Ferroni,48a,††A. Pilloni,48a,48bG. Piredda,48a,‡
C. Bünger,49 S. Dittrich,49O. Grünberg,49M. Heß,49T. Leddig,49C. Voß,49R. Waldi,49T. Adye,50 F. F. Wilson ,50 S. Emery,51G. Vasseur,51D. Aston,52C. Cartaro,52M. R. Convery,52J. Dorfan,52W. Dunwoodie,52M. Ebert,52 R. C. Field,52B. G. Fulsom,52M. T. Graham,52C. Hast,52W. R. Innes,52,‡ P. Kim,52D. W. G. S. Leith,52,‡ S. Luitz,52
D. B. MacFarlane,52D. R. Muller,52 H. Neal,52B. N. Ratcliff,52A. Roodman,52 M. K. Sullivan,52 J. Va’vra,52 W. J. Wisniewski,52M. V. Purohit,53J. R. Wilson,53A. Randle-Conde,54S. J. Sekula,54H. Ahmed,55M. Bellis,56 P. R. Burchat,56E. M. T. Puccio,56M. S. Alam,57J. A. Ernst,57R. Gorodeisky,58N. Guttman,58D. R. Peimer,58A. Soffer,58 S. M. Spanier,59J. L. Ritchie,60R. F. Schwitters,60J. M. Izen,61X. C. Lou,61F. Bianchi,62a,62bF. De Mori,62a,62bA. Filippi,62a
D. Gamba,62a,62b L. Lanceri,63L. Vitale,63F. Martinez-Vidal,64A. Oyanguren,64J. Albert,65b A. Beaulieu,65b F. U. Bernlochner,65b G. J. King,65bR. Kowalewski,65bT. Lueck,65bI. M. Nugent,65bJ. M. Roney,65b R. J. Sobie,65a,65b
N. Tasneem,65b T. J. Gershon,66 P. F. Harrison,66T. E. Latham,66R. Prepost,67 and S. L. Wu67 (BABAR Collaboration)
1
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universit´e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France
2
Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain 3INFN Sezione di Bari and Dipartimento di Fisica, Universit `a di Bari, I-70126 Bari, Italy
4
University of Bergen, Institute of Physics, N-5007 Bergen, Norway
5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 6
Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany 7aInstitute of Particle Physics, Vancouver, British Columbia, Canada V6T 1Z1 7b
University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 8aBudker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia
8b
Novosibirsk State University, Novosibirsk 630090, Russia 8cNovosibirsk State Technical University, Novosibirsk 630092, Russia
9
University of California at Irvine, Irvine, California 92697, USA 10University of California at Riverside, Riverside, California 92521, USA 11
University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA 12California Institute of Technology, Pasadena, California 91125, USA
13
15Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France 16a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
16bDipartimento di Fisica e Scienze della Terra, Universit `a di Ferrara, I-44122 Ferrara, Italy 17
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy 18INFN Sezione di Genova, I-16146 Genova, Italy 19
Harvey Mudd College, Claremont, California 91711, USA
20Humboldt-Universität zu Berlin, Institut für Physik, D-12489 Berlin, Germany 21
Indian Institute of Technology Guwahati, Guwahati, Assam 781 039, India 22University of Iowa, Iowa City, Iowa 52242, USA
23
Iowa State University, Ames, Iowa 50011, USA 24Johns Hopkins University, Baltimore, Maryland 21218, USA 25
Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France 26Lawrence Livermore National Laboratory, Livermore, California 94550, USA
27
University of Liverpool, Liverpool L69 7ZE, United Kingdom 28Queen Mary, University of London, London E1 4NS, United Kingdom 29
University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom
30
University of Louisville, Louisville, Kentucky 40292, USA
31Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany 32
University of Manchester, Manchester M13 9PL, United Kingdom 33University of Maryland, College Park, Maryland 20742, USA 34
Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA
35a
Institute of Particle Physics, Montr´eal, Qu´ebec, Canada H3A 2T8 35bMcGill University, Montr´eal, Qu´ebec, Canada H3A 2T8
36a
INFN Sezione di Milano, I-20133 Milano, Italy
36bDipartimento di Fisica, Universit `a di Milano, I-20133 Milano, Italy 37
University of Mississippi, University, Mississippi 38677, USA
38Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7 39
INFN Sezione di Napoli and Dipartimento di Scienze Fisiche, Universit `a di Napoli Federico II, I-80126 Napoli, Italy
40
NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands
41
University of Notre Dame, Notre Dame, Indiana 46556, USA 42Ohio State University, Columbus, Ohio 43210, USA
43a
INFN Sezione di Padova, I-35131 Padova, Italy
43bDipartimento di Fisica, Universit `a di Padova, I-35131 Padova, Italy 44
Laboratoire de Physique Nucl´eaire et de Hautes Energies, Sorbonne Universit´e, Paris Diderot Sorbonne Paris Cit´e, CNRS/IN2P3, F-75252 Paris, France
45a
INFN Sezione di Perugia, I-06123 Perugia, Italy
45bDipartimento di Fisica, Universit `a di Perugia, I-06123 Perugia, Italy 46a
INFN Sezione di Pisa, I-56127 Pisa, Italy
46bDipartimento di Fisica, Universit `a di Pisa, I-56127 Pisa, Italy 46c
Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy 47Princeton University, Princeton, New Jersey 08544, USA
48a
INFN Sezione di Roma, I-00185 Roma, Italy
48bDipartimento di Fisica, Universit `a di Roma La Sapienza, I-00185 Roma, Italy 49
Universität Rostock, D-18051 Rostock, Germany
50Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom 51
IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France 52SLAC National Accelerator Laboratory, Stanford, California 94309, USA
53
University of South Carolina, Columbia, South Carolina 29208, USA 54Southern Methodist University, Dallas, Texas 75275, USA 55
St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5 56Stanford University, Stanford, California 94305, USA
57
State University of New York, Albany, New York 12222, USA 58Tel Aviv University, School of Physics and Astronomy, Tel Aviv 69978, Israel
59
University of Tennessee, Knoxville, Tennessee 37996, USA 60University of Texas at Austin, Austin, Texas 78712, USA 61
62aINFN Sezione di Torino, I-10125 Torino, Italy 62b
Dipartimento di Fisica, Universit `a di Torino, I-10125 Torino, Italy
63INFN Sezione di Trieste and Dipartimento di Fisica, Universit `a di Trieste, I-34127 Trieste, Italy 64
IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain 65aInstitute of Particle Physics, Victoria, British Columbia, Canada V8W 3P6
65b
University of Victoria, Victoria, British Columbia, Canada V8W 3P6 66Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
67
University of Wisconsin, Madison, Wisconsin 53706, USA
(Received 21 April 2020; accepted 26 May 2020; published 15 June 2020)
We present a search for seven lepton-flavor-violating neutral charm meson decays of the type D0→ X0eμ∓, where X0 represents a π0, K0S, ¯K0, ρ0, ϕ, ω, or η meson. The analysis is based on 468 fb−1of eþe−annihilation data collected at or close to theϒð4SÞ resonance with the BABAR detector at the SLAC National Accelerator Laboratory. No significant signals are observed, and we establish 90% confidence level upper limits on the branching fractions in the rangeð5.0 − 22.5Þ × 10−7. The limits are between 1 and 2 orders of magnitude more stringent than previous measurements.
DOI:10.1103/PhysRevD.101.112003
I. INTRODUCTION
Lepton-flavor-conserving charm decays such as D → Xeþe− or D → Xμþμ−, where X is a meson, can occur in the standard model (SM) through short-distance[1,2]and long-distance[2]processes. Short-distance processes con-tribute to the D → Xeþe− and D → Xμþμ− branching fractions at the order Oð10−9Þ, while long-distance proc-esses contribute at a level as high asOð10−6Þ. In contrast, the lepton-flavor-violating (LFV) neutral charm decays D0→ X0eμ∓, where X0is a neutral meson, are effectively forbidden in the SM because they can occur only through lepton-flavor mixing[3]and are therefore suppressed to the orderOð10−50Þ. As such, the decays D0→ X0eμ∓should not be visible with current data samples. However, new-physics models, such as those involving Majorana neu-trinos, leptoquarks, and two-Higgs doublets, allow for lepton number and lepton flavor to be violated [4–8]. Some models make predictions for, or use constraints from,
three-body decays of the form D → Xl0l or B → Xl0l, where l and l0 represent an electron or muon [1,6,7, 9–12]. Most recent theoretical work has targeted the charged charm decays Dþ → Xþl0þl−. For example, Ref.[4]estimates that BðDþ→ πþμe∓Þ can be as large as2 × 10−6for certain leptoquark couplings. Some models that consider LFV and lepton-number-violating four-body charm decays, with two leptons and two hadrons in the final state, predict branching fractions up toOð10−5Þ, approach-ing those accessible with current data[6–8,13].
The branching fractionsBðD0→ h0−hþμþμ−Þ, where h0 and h represent a K or π meson, and BðD0→ K−πþeþe−Þ have recently been measured to be Oð10−7Þ to Oð10−6Þ [14–16], compatible with SM predictions [17,18]. The branching fractions for the decays D0→ X0eþe− and D0→ X0μþμ− have not yet been measured. However, 90% confidence level (C.L.) upper limits on the branching fractions do exist and are in the rangeð0.3 − 10Þ × 10−5for D0→ X0eþe− and ð3.2 − 53Þ × 10−5 for D0→ X0μþμ− [19–22]. It is likely that one or more of these decays are a major contributor to the branching fractions of the decays D0→ h0−hþeþe− or D0→ h0−hþμþμ−, as long-distance processes are predicted to be dominant[2], and published distributions of the invariant masses mðh0−hþÞ for D0→ h0−hþμþμ− and D0→ K−πþeþe− indicate large yields near some of the X0 invariant masses[14–16].
The most stringent existing upper limits on the branching fractions for the LFV four-body decays of the type D0→ h0−hþeμ∓are in the rangeð11.0–19.0Þ × 10−7at the 90% confidence level[23]. For the LFV decays D0→ X0eμ∓, where X0is an intermediate resonance meson decaying to h0−hþ,πþπ−π0orγγ, the 90% C.L. limits are in the range ð3.4–118Þ × 10−5 [20,21,24]. For the D0→ X0eμ∓
decays with the same final state as the D0→ h0−hþeμ∓ *Deceased.
†Present address: Wuhan University, Wuhan 430072, China. ‡Present address: Universit`a di Bologna and INFN Sezione di Bologna, I-47921 Rimini, Italy.
§Present address: King’s College, London WC2R 2LS, United Kingdom.
∥Present address: University of Huddersfield, Huddersfield HD1 3DH, United Kingdom.
¶Present address: University of South Alabama, Mobile, Alabama 36688, USA.
decays (D0→ K0Sð→ πþπ−Þeμ∓, D0→ ρ0ð→ πþπ−Þeμ∓, D0→ ¯K0ð→ K−πþÞeμ∓, and D0→ ϕð→ KþK−Þeμ∓), the current D0→ X0eμ∓branching fraction upper limits, which are in the range ð3.4–8.3Þ × 10−5 [20,21,24], are approximately 20 times less stringent than the D0→ h0−hþeμ∓ limits reported in Ref.[23].
In this paper, we present a search for seven D0→ X0eμ∓ LFV decays, where X0represents aπ0, K0S, ¯K0,ρ0,ϕ, ω, or η meson, with data recorded with the BABAR detector at the PEP-II asymmetric-energy eþe− collider operated at the SLAC National Accelerator Laboratory. The intermediate mesons X0are reconstructed through the decaysπ0→ γγ, K0S→ πþπ−, ¯K0→ K−πþ, ρ0→ πþπ−, ϕ → KþK−, ω → πþπ−π0, η → πþπ−π0, and η → γγ. The branching
fractions for the signal modes are measured relative to the normalization decays D0→ π−πþπþπ− (for X0¼ K0S; ρ0; ω), D0→ K−πþπþπ− (X0¼ ¯K0), and D0→
K−Kþπþπ−(X0¼ ϕ). For X0¼ π0orη, the normalization mode D0→ K−πþπþπ− is used as it has the smallest branching fraction uncertainty[24]and the largest number of reconstructed candidates of the three normalization modes. Although decays of the type D0→ X0h0−hþ have momentum distributions that more closely follow those of the signal decays under study, they suffer from smaller branching fractions, greater uncertainties on their branching fractions, and reduced reconstruction efficiencies relative to the three chosen normalization modes.
The D0 mesons are identified using the decay Dþ→ D0πþproduced in eþe−→ c¯c events. Although D0mesons are also produced via other processes, the use of this decay chain increases the purity of the D0samples at the cost of a smaller number of reconstructed D0 mesons.
II. THEBABAR DETECTOR AND DATA SET The BABAR detector is described in detail in Refs.[25,26]. Charged particles are reconstructed as tracks with a five-layer silicon vertex detector and a 40-layer drift chamber inside a 1.5 T solenoidal magnet. An electromag-netic calorimeter comprising 6580 CsI(Tl) crystals is used to identify and measure the energies of electrons, positrons, muons, and photons. A ring-imaging Cherenkov detector is used to identify charged hadrons and to provide additional lepton identification information. Muons are primarily identified with an instrumented magnetic-flux return.
The data sample corresponds to 424 fb−1 of eþe− collisions collected at the center-of-mass (c.m.) energy of the ϒð4SÞ resonance (10.58 GeV, on peak) and an additional 44 fb−1 of data collected 0.04 GeV below the ϒð4SÞ resonance (off peak)[27].
Monte Carlo (MC) simulation is used to investigate sources of background contamination and evaluate selec-tion efficiencies. Simulated events are also used to validate the selection procedure and for studies of systematic
effects. The signal and normalization channels are simu-lated with theEvtGenpackage[28]. We generate the signal
channel decays uniformly throughout the three-body phase space, while the normalization modes include two-body and three-body intermediate resonances, as well as non-resonant decays. We also generate eþe− → q¯q (q ¼ u, d, s, c), Bhabha and μþμ−pairs (collectively referred to as QED events), and B ¯B background, using a combination of the
EvtGen,Jetset[29],KK2F[30],AfkQed[31], andTAUOLA[32]
generators, where appropriate. The background samples are produced with an integrated luminosity approximately 6 times that of the data. Final-state radiation is generated usingPHOTOS[33]. The detector response is simulated with
GEANT4[34,35]. All simulated events are reconstructed in the same manner as the data.
III. EVENT SELECTION
In the following, unless otherwise noted, all observables are evaluated in the laboratory frame. In order to optimize the event reconstruction, candidate selection criteria, multi-variate analysis training, and fit procedure, a rectangular area in the mðD0Þ versus Δm ¼ mðDþÞ − mðD0Þ plane is defined, where mðDþÞ and mðD0Þ are the reconstructed masses of the Dþ and D0 candidates, respectively. This region is kept hidden (blinded) in data until the analysis steps are finalized. The hidden region is approximately 3 times the root-mean-square (rms) width of the Δm and mðD0Þ resolutions. Its Δm region is 0.1447 < Δm < 0.1462 GeV=c2 for all modes. The mðD0Þ signal peak
distribution is asymmetric due to bremsstrahlung emission, with the left-side rms width typically1–2 MeV=c2 wider than the right side. The mðD0Þ RMS widths vary between 5 and21 MeV=c2, depending on the signal mode.
(e.g., muon) that are in reality of a different flavor (i.e., not a muon), is typically less than 0.03 for all selection criteria, except for the pion selection criteria, where the muon misidentification rate can be as high as 0.35 at low momentum.
We select events that have at least five charged tracks, except for D0→ π0eμ∓and D0→ ηð→ γγÞeμ∓, which must have at least three. Two or more of the tracks must be identified as leptons. The separation along the beam axis between the two leptons at their distance of closest approach to the beam line is required to be less than 0.2 cm. The leptons must have opposite charges, and their momenta must be greater than 0.3 GeV=c. Electrons and positrons from photon conversions are rejected by remov-ing electron-positron pairs with an invariant mass less than 0.03 GeV=c2and a production vertex more than 2 cm from
the beam axis.
The minimum photon energy in a signal decay is required to be greater than 0.025 GeV. For the decays D0→ π0eμ∓and D0→ ηð→ γγÞeμ∓, the momentum of theπ0
orη must be greater than 0.4 GeV=c and the energy of each photon from theπ0must be greater than 0.045 GeV. The reconstructed π0 invariant mass for all signal decays is required to be between 120 and 160 MeV=c2.
The reconstructed invariant masses of the π0, K0S, ¯K0, ρ0,ϕ, and ω candidates are required to be within 19, 9, 76,
240, 20, and 34 MeV=c2, of their nominal mass [24], respectively. For the decays η → γγ and η → πþπ−π0, the invariant mass of theη candidates must be within 47 and 35 MeV=c2 of the η nominal mass, respectively. These
ranges are equivalent to 3 times the reconstructed RMS widths.
Candidate D0 mesons for the signal modes are formed from the electron or positron, muon or antimuon, and intermediate resonance candidates. For the normalization modes, the D0 candidate is formed from four charged tracks. Particle identification is applied to all charged tracks and the D0 candidates are reconstructed with the appro-priate charged-track mass hypotheses for both the signal and normalization decays. The tracks are required to form a good-quality vertex with anχ2probability for the vertex fit greater than 0.005. For the decay D0→ K0Seμ∓, K0Smust have a transverse flight distance from the D0decay vertex greater than 0.2 cm. A bremsstrahlung energy recovery algorithm is applied to electrons and positrons, in which the energy of photon showers that are within a small angle (35 mrad in polar angle and 50 mrad in azimuth[25]) with respect to the tangent of the initial electron or positron direction is added to the energy of the electron or positron candidate. For the normalization modes, the reconstructed D0 meson mass is required to be in the range 1.81 < mðD0Þ < 1.91 GeV=c2, while for the signal modes, mðD0Þ must be in the hidden mðD0Þ range defined above.
The candidate Dþ is formed by combining the D0 candidate with a charged pion having a momentum greater
than 0.1 GeV=c. For the normalization mode D0→ K−πþπþπ−, this pion is required to have a charge opposite that of the kaon. The pion and D0candidate are subject to a vertex fit, with the D0mass constrained to its known value [24]and the requirement that the D0 meson and the pion originate from the beam spot[37]. Theχ2probability of the fit is required to be greater than 0.005. After the application of the Dþ vertex fit, the D0 candidate momentum in the c.m. system pðD0Þ must be greater than 2.4 GeV=c. For the normalization modes, the mass difference Δm is required to be0.143 < Δm < 0.148 GeV=c2, while for the signal modes the range is0.1395 < Δm < 0.1610 GeV=c2. The extended Δm range for the signal modes provides greater stability when fitting the background distributions. The requirement on the number of charged tracks strongly suppresses backgrounds from QED processes. The pðD0Þ criterion removes most sources of combina-torial background, as well as charm hadrons produced in B decays, which are kinematically limited to pðD0Þ ≲ 2.2 GeV=c[38].
Simulated samples indicate that the remaining back-ground arises from eþe− → c¯c events in which charged tracks and neutral particles can either be lost or selected from elsewhere in the event to form a D0 candidate. To reject this background, a multivariate selection based on a boosted decision tree (BDT) discriminant is applied to the signal modes[39]. A common set of eight input observ-ables is used for all modes: the momenta of the electron or positron, muon or antimuon, and reconstructed inter-mediate meson; the momentum of the lowest-momentum charged track or photon from the X0 candidate; the maximum angle between the direction of D0 daughters and the D0 direction; the total energy of all charged tracks and photons in the event, normalized to the beam energy; the ratio xp¼ pðDþÞ=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E2eþe−−m2ðDþÞ
q
, where pðDþÞ is the c.m. momentum of the Dþ candidate and Eeþe− is the c.m. beam energy; and the reconstructed mass
of the intermediate meson. Three additional input observ-ables are used for the D0 decays with ω or η decaying to πþπ−π0: the momentum and reconstructed mass of theπ0
candidate, and the energy of the lowest-energy photon from theπ0. The discriminant is trained and tested independently for each signal mode, using simulated samples for the signal modes, and ensembles of data outside the hidden region and eþe− → c¯c simulated samples for the back-ground. The discriminant output selection point is chosen using the Punzi figure of merit,ϵsig=ð
ffiffiffiffiffiffi Nb
p
þ 2.5Þ, where ϵsig is the signal reconstruction efficiency for simulated
signal and Nbis the number of background candidates[40].
The cross feed to one signal mode from any other signal modes is estimated from simulated samples to be less than 4% in all cases, and typically less than 1%, assuming equal branching fractions for all signal modes. The cross feed to a specific normalization mode from the other two normalization modes is predicted from simulation to be less than 0.7%, where the branching fractions are taken from Ref. [24]. The percentage of normalization mode Dþ candidates constructed from a true D0decay and an incorrect charged pion is estimated from simulation studies to be less than 1% and is ignored in the extraction of the normalization mode yield. Simulation studies show that background from SM-allowed D0 decays such as D0→ h0hh0h and D0→ X0h0h, which are suppressed by the lepton PID criteria, is not expected for most signal modes. The exception is D0→ ρ0eμ∓, where0.3 0.2 events are predicted from D0→ π−πþπþπ− decays. The statistical uncertainty arises from the limited size of the simulation sample. This potential cross feed is not considered in the extraction of the signal yield. In the data, no events with reconstructed normalization decays contain reconstructed signal decays.
From the data, we find that the fraction of normalization mode events with more than one candidate is 2.4%, 3.6%, and 4.4% for D0→ K−Kþπþπ−, D0→ K−πþπþπ−, and D0→ π−πþπþπ−, respectively. For the signal mode with η → πþπ−π0, 40% of events have multiple candidates. For
η → γγ and ω decays, the number of events with multiple candidates is∼10%, and for the remaining modes it is 1%– 5%. The number of multiple candidates in the simulation and data samples agree within a relative 2%. If two or more candidates are found in an event, the one with the highest Dþvertex χ2probability is selected. After apply-ing the best-candidate selection, the correct Dþcandidate in the simulated samples is selected with a probability of 95% or more for the normalization modes. For the signal modes, 70% of Dþ candidates are correctly selected for η → πþπ−π0, and between 86% and 94% for the remaining
modes. After the application of all selection criteria and corrections for small differences between data and MC simulation in tracking and PID performance, the recon-struction efficiency ϵsig for the simulated signal decays is
between 1.6% and 3.6%, depending on the mode. For the normalization decays, the reconstruction efficiencyϵnormis between 19.2% and 24.7%. The difference betweenϵsigand ϵnormis mainly due to the minimum momentum criterion on
the leptons required by the PID algorithms [26]. IV. SIGNAL YIELD EXTRACTION
The D0→ X0eμ∓ signal mode branching fractionBsig
is determined relative to that of the normalization decay using Bsig¼ Nsig Nnorm ϵnorm ϵsig Lnorm Lsig Bnorm BðX0Þ; ð1Þ
whereBnormis the branching fraction of the normalization
mode[24], and Nsig and Nnorm are the fitted yields of the
signal and normalization mode decays, respectively.BðX0Þ is the branching fraction of the intermediate meson decay channel. The symbols Lsig and Lnorm represent the
inte-grated luminosities of the data samples used for the signal (468.2 2.0 fb−1) and the normalization decays
(39.3 0.2 fb−1), respectively[27]. For the signal modes, we use both the on-peak and off-peak data samples. For the normalization modes, a subset of the off-peak data is sufficient for achieving statistical uncertainties that are much smaller than the systematic uncertainties.
We perform an extended unbinned maximum-likelihood fit to extract the signal and background yields for both the normalization and signal modes [41]. The likelihood function is L ¼ 1 N!exp −X2 j¼1 nj YN i¼1 X2 j¼1 njPjð⃗xi; ⃗αjÞ : ð2Þ We define the likelihood for each event candidate i to be the sum of njPjð⃗xi; ⃗αjÞ over two hypotheses j (signal or
normalization and background). The symbolPjð⃗xi; ⃗αjÞ is the product of the probability density functions (PDFs) for hypothesis j evaluated for the measured variables ⃗xiof the
ith event. The total number of events in the sample is N, and nj is the yield for hypothesis j. The quantities ⃗αj
represent parameters of Pj. The distributions of each discriminating variable xi in the likelihood function is
modeled with one or more PDFs, where the parameters⃗αj are determined from fits to signal simulation or data samples.
Each normalization mode yield Nnorm is extracted by
performing a two-dimensional unbinned maximum-likelihood fit to the Δm versus mðD0Þ distributions in the range 0.143 < Δm < 0.148 GeV=c2 and 1.81 < mðD0Þ < 1.91 GeV=c2. Considering normalization and background events separately, the measured Δm and mðD0Þ values are essentially uncorrelated and are therefore treated as independent observables in the fits. The PDFs in the fits depend on the normalization mode and use sums of multiple Cruijff[16]and Crystal Ball[42]functions in both Δm and mðD0Þ. The functions for each observable use a
common mean. The background is modeled with an ARGUS threshold function [43] for Δm and a Chebyshev polynomial for mðD0Þ. The ARGUS end point parameter is fixed at 0.1395 GeV=c2, the Δm kinematic threshold for Dþ→ D0πþ decays. All yields and PDF parameters, apart from the ARGUS end point parameter, are allowed to vary in the fit.
normalization modes in the range 0.143 < Δm < 0.148 GeV=c2.
After the application of the selection criteria, there are on the order of 100 events or fewer available for fitting in each signal mode. Each signal mode yield Nsig is
therefore extracted by performing a one-dimensional unbinned maximum-likelihood fit to Δm in the range 0.1395 < Δm < 0.1610 GeV=c2. A Cruijff function is
implemented for the signal mode PDF, except for D0→ ϕeμ∓, for which two two-piece Gaussians func-tions are used, and D0→ ρ0eμ∓, for which two Cruijff functions are used. The background is modeled with an ARGUS function with the same end point used for the normalization modes. The signal PDF parameters and the end point parameter are fixed in the fit. All other back-ground parameters and the signal and backback-ground yields are allowed to vary. Figure2shows the results of the fits to the Δm distributions for the signal modes.
We test the performance of the maximum-likelihood fit for the normalization modes by generating ensembles of MC samples from the normalization and background PDF distributions. The mean numbers of normalization and background candidates used in the ensembles are taken from the fits to the data. The numbers of generated back-ground and normalization mode candidates are sampled from a Poisson distribution. All background and normali-zation mode PDF parameters are allowed to vary, except for the ARGUS function end point. No significant biases are observed in the fitted yields of the normalization modes. The same procedure is repeated for the maximum-likelihood fits to the signal modes, with ensembles of MC samples generated from the background PDF distributions only, assuming a signal yield of zero. The signal PDF parameters are fixed to the values used for the fits to the data, and the signal yield is allowed to vary. The biases in the fitted signal yields are less than0.3 candidates for all modes, and these are subtracted from the fitted yields before calculating the signal branching fractions.
To confirm the normalization procedure, the signal modes in Eq.(1)are replaced with the decay D0→ K−πþ, which has a well-measured branching fraction[24]. The D0→ K−πþ decays are reconstructed using the on-peak data sample only (424.3 1.8 fb−1). The D0→ K−πþdecay is selected using the same criteria as used for the D0→ K−πþπþπ− mode, which is used as the normalization mode for this
test. The D0→K−πþ signal yield is18819501380 with ϵsig¼ð27.40.2Þ%. Thus, we determine BðD0→ K−πþÞ ¼
ð3.98 0.08 0.10Þ%, where the uncertainties are statis-tical and systematic, respectively. This is consistent with the current world average ofð3.95 0.03Þ%[24]. When the test is repeated using either D0→ K−Kþπþπ− or D0→ π−πþπþπ− as the normalization mode,BðD0→ K−πþÞ is
determined to beð3.51 0.18 0.18Þ% and ð4.12 0.13 0.16Þ%, respectively. 0.143 0.144 0.145 0.146 0.147 0.148 ] 2 [GeV/c m Δ 100 200 300 ) 2 Candidates / (0.05 MeV/c Data Total Signal Background R A B A B (a) − π + π + K − K → 0 D 0.143 0.144 0.145 0.146 0.147 0.148 ] 2 [GeV/c m Δ 2000 4000 ) 2 Candidates / (0.03 MeV/c Data Total Signal Background R A B A B (b) − π + π + π − K → 0 D 0.143 0.144 0.145 0.146 0.147 0.148 ] 2 [GeV/c m Δ 500 1000 1500 ) 2 Candidates / (0.05 MeV/c Data Total Signal Background R A B A B (c) − π + π + π − π → 0 D
FIG. 1. Projections of the unbinned maximum-likelihood fits to the final candidate distributions as a function of Δm for the normalization modes in the range0.143 < Δm < 0.148 GeV=c2. The solid blue line is the total fit, the dashed red line is the signal, and the dotted green line is the background.
TABLE I. Summary of fitted candidate yields, with statistical uncertainties, and reconstruction efficiencies for the three nor-malization modes.
V. SYSTEMATIC UNCERTAINTIES
The systematic uncertainties in the branching fraction determinations of the signal modes arise from so-called additive systematic uncertainties that affect the significance of the signal mode yields in the fits to the data samples and from multiplicative systematic uncertainties on the lumi-nosity and signal reconstruction efficiencies.
The main sources of the additive systematic uncertainties in the signal yields are associated with the model para-metrizations used in the fits to the signal modes, the
allowed invariant-mass ranges for the D0 and X0 candi-dates, the fit biases, the amount of cross feed, and the limited MC and data sample sizes available for the optimization of the BDT discriminants.
The uncertainties associated with the fit model para-metrizations of the signal modes are estimated by repeating the fits with alternative PDFs. This involves replacing the Cruijff functions with Crystal Ball functions, using a two-piece Gaussian function, and changing the number of functions used in the PDFs. For the background, the ARGUS function is replaced by a first- or second-order polynomial. The largest deviation occurs when using the Crystal Ball functions for the signal and the first-order polynomial for the background. The systematic uncertainty is taken as half this maximum deviation. The largest contribution comes from the normalization mode D0→ π−πþπþπ− due to the presence of increased background
and greater uncertainty in the background shape.
Changes in the D0and X0invariant-mass selection criteria can affect the signal mode yields and the fitted function parameters. To investigate this effect, we change the D0and X0invariant-mass selection ranges by0.5σ, where σ is the rms width of the mass of the D0or X0meson, and repeat the fits for the signal mode yields. The systematic uncertainty is taken as half the maximum deviation.
The systematic uncertainties in the correction on the fit biases for the signal yields are taken from the ensembles of fits to the MC samples. Given the central value of the signal yield obtained from the fit in each mode, the cross feed yields from all other modes are calculated and are taken as a systematic uncertainty. To evaluate the systematic uncer-tainty in the application of the BDT discriminant, we vary the value of the selection criterion for the BDT discriminant output, change the size of the hidden region in data, and also retrain the BDT discriminant using a training sample with a different ensemble of MC samples. Summing the uncertainties in quadrature, the total additive systematic uncertainties in the signal yields are between 0.4 and 0.9 events.
Multiplicative systematic uncertainties are due to assump-tions made about the distribuassump-tions of the final-state particles in the signal simulation modeling, the model parametriza-tions used in the fits to the normalization modes, the normalization mode branching fractions, tracking and PID efficiencies, limited simulation sample sizes, and luminosity. Since the decay mechanism of the signal modes is unknown, we vary the angular distributions of the simu-lated final-state particles from the D0signal decay in three angular variables, defined following the prescription of Ref. [44]. We weight the events, which are simulated uniformly in phase space, using combinations of sin, cos, sin2, and cos2 functions of the angular variables. The reconstruction efficiencies calculated from simulation sam-ples as functions of the three angles are constant, within the statistics available. The deviations of the reweighted Data Total Signal Background 0.14 0.145 0.15 0.155 0.16 ] 2 [GeV/c m Δ 5 10 ) 2 Entries / (0.88 MeV/c R A B A B ± μ ± e 0 π → 0 D R A B A B ± μ ± e S 0 K → 0 D 0.14 0.145 0.15 0.155 0.16 ] 2 [GeV/c m Δ 5 10 ) 2 Entries / (0.88 MeV/c R A B A B ± μ ± e *0 K → 0 D R A B A B ± μ ± e 0 ρ → 0 D ] 5 10 ) 2 Entries / (0.88 MeV/c R A B A B ± μ ± e φ → 0 D R A B A B ± μ ± e ω → 0 D 0.14 0.145 0.15 0.155 ] 2 [GeV/c m Δ 5 10 ) 2 Entries / (0.88 MeV/c R A B A B ± μ ± )e γ γ → ( η → 0 D 0.145 0.15 0.155 0.16 ] 2 [GeV/c m Δ R A B A B ± μ ± )e 0 π − π + π → ( η → 0 D
efficiencies from the default average reconstruction effi-ciencies are therefore small. Half the maximum change in the average reconstruction efficiency is assigned as a systematic uncertainty.
The reconstruction efficiency of the simulated signal samples generally increases with increasing dilepton invariant mass mðeμ∓Þ. To account for the scenario in which a signal appears at a specific mðeμ∓Þ, the simulated signal reconstruction efficiency is calculated in 20 subregions of mðeμ∓Þ for each signal mode. The standard deviation of the 20 efficiencies is then taken as a systematic uncertainty.
Uncertainties associated with the fit model parametriza-tions of the normalization modes are estimated by repeating the fits with alternative PDFs. This involves swapping the
Cruijff and Crystal Ball functions used in both Δm and mðD0Þ. For the background, the order of the polynomials is changed and the ARGUS function is replaced by a second-order polynomial. Half the maximum change in the fitted yield is assigned as a systematic uncertainty. The normali-zation modes branching fraction uncertainties are taken from Ref.[24].
For both signal and normalization modes, we include uncertainties to account for discrepancies between recon-struction efficiencies calculated from simulation and data samples of 1.0% per K0S, 0.8% per lepton, and 0.7% per hadron track[45]. We include a momentum-dependent π0 reconstruction efficiency uncertainty of 2.1% for D0→ π0eμ∓ and 2.3% for D0→ ωeμ∓ and D0→
ηð→ πþπ−π0Þeμ∓. For the PID efficiencies, we assign an
uncertainty of 0.7% per track for electrons, 1.0% for muons, 0.2% for charged pions, and 1.1% for kaons [26]. A systematic uncertainty of 0.4% is associated with our knowl-edge of the luminosities Lnorm and Lsig [27]. We assign
systematic uncertainties in the range 0.8%–1.8% to account for the limited size of the simulation samples available for calculating reconstruction efficiencies for the signal and normalization modes.
The simulation samples for the normalization modes contain a resonant structure of intermediate resonances that decay to two- or three-body final states, as well as four-body nonresonant decays. To investigate how changes in the resonant structure affect the reconstruction efficiencies, the simulation samples were generated using a four-body phase-space distribution only and the reconstruction TABLE II. Summary of the contributions to the systematic
uncertainties on the signal mode branching fractions, as defined in Eq.(1), that arise from uncertainties in the measurement of the normalization modes. π−πþπþπ− K−πþπþπ− K−Kþπþπ− PDF variation 4.6% 1.0% 1.0% K0S correction 1.0% 1.0% 1.0% Tracking correction 3.5% 3.5% 3.5% PID correction 0.8% 1.7% 2.6% Luminosity 0.4% 0.4% 0.4% NormalizationB 3.0% 1.8% 4.5% Simulation size 1.0% 1.0% 0.8% Total 6.8% 4.7% 6.6%
TABLE III. Summary of D0→ X0eμ∓additive and multiplicative systematic uncertainties, excluding those due to the normalization modes given in TableII.
X0¼ π0 K0S ¯K0 ρ0 ϕ ω η η X0→ γγ πþπ− K−πþ πþπ− KþK− πþπ−π0 γγ πþπ−π0 Additive (events): PDF variation 0.23 0.05 0.20 0.16 0.17 0.26 0.43 0.16 Fit bias 0.09 0.28 0.21 0.15 0.24 0.09 0.08 0.07 D0=X0mass 0.30 0.04 0.05 0.07 0.07 0.07 0.04 0.23 BDT discriminant 0.83 0.68 0.71 0.30 0.06 0.35 0.27 0.58 Cross feed 0.01 0.06 Subtotal (candidates) 0.92 0.74 0.76 0.38 0.31 0.45 0.52 0.65 Multiplicative (%): Angular variation 1.4 2.8 2.0 3.4 5.3 1.9 1.6 1.6 mðeμ∓Þ dependence 3.0 3.9 5.1 6.5 3.5 4.1 4.2 5.6 BðX0Þ subdecay 0.1 1.0 0.8 0.5 1.2 K0S correction 1.0 Tracking correction 2.3 3.7 3.7 3.7 3.7 3.7 2.3 3.7 PID correction 2.7 2.1 3.0 2.1 3.9 3.1 2.7 3.1 π0 correction 2.1 2.3 2.3 Luminosity 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
Simulation sample size 1.4 1.3 1.5 1.3 1.4 1.8 1.3 1.5
efficiencies recalculated. The resulting changes in reconstruction efficiencies are less than the statistical uncertainties on ϵnorm due to the limited size of the
simulation samples, and no systematic uncertainties are assigned. The total multiplicative systematic uncertainties are between 4.7% and 6.8% for the normalization modes and between 5.2% and 8.6% for the signal modes.
TableIIsummarizes the contributions of the systematic uncertainties of the normalization modes to the systematic uncertainties in the signal mode branching fractions, as defined in Eq. (1). Table III summarizes the systematic uncertainties in the signal mode yields, excluding those due to the normalization modes.
VI. RESULTS
Table IV gives the fitted signal yields, reconstruction efficiencies, branching fractions with statistical and system-atic uncertainties, 90% C.L. upper limits on the branching fractions, and previous upper limits[20,21,24]for the signal modes. The yields for all the signal modes are compatible with zero. We assume that there are no cancellations due to correlations in the systematic uncertainties in the numerator and denominator of Eq.(1). We use the frequentist approach of Feldman and Cousins[46]to determine 90% C.L. bands. When computing the limits, the systematic uncertainties are combined in quadrature with the statistical uncertainties in the fitted signal yields.
Only two of the modes, D0→ ρ0eμ∓ and D0→ ¯K0eμ∓, share events with the fitted samples used in
Ref. [23] to measure the branching fractions for D0→ π−πþeμ∓and D0→ K−πþeμ∓, respectively. Fourteen of
the 46 events in the D0→ ρ0eμ∓ sample are shared with the 151 events used in the D0→ π−πþeμ∓sample and 4 of the 24 events in the D0→ ¯K0eμ∓ sample are shared with the 68 events used in the D0→ K−πþeμ∓ sample.
In summary, we report 90% C.L. upper limits on the branching fractions for seven lepton-flavor-violating D0→ X0eμ∓ decays. The analysis is based on a sample of eþe− annihilation data collected with the BABAR detector, corresponding to an integrated luminosity of 468.2 2.0 fb−1. The limits are in the rangeð5.0–22.5Þ ×
10−7 and are between 1 and 2 orders of magnitude more
stringent than previous D0→ X0eμ∓ decay results. For the four D0→ X0eμ∓decays with the same final state as the D0→ h0−hþeμ∓ decays reported in Ref. [23], the limits are 1.5–3 times more stringent.
ACKNOWLEDGMENTS
We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them. This work is supported by the U.S. Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat `a l’Energie Atomique and Institut National de Physique Nucl´eaire et de Physique des Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Economía y Competitividad (Spain), the Science and Technology Facilities Council (United Kingdom), and the Binational Science Foundation (U.S.-Israel). Individuals have received support from the Marie-Curie IEF program (European Union) and the A. P. Sloan Foundation (USA).
TABLE IV. Summary of fitted signal yields Nsigwith statistical and systematic uncertainties, reconstruction efficienciesϵsig, branching fractions with statistical and systematic uncertainties, 90% C.L. upper limits (U.L.) on the branching fractions, and previous limits
[20,21,24]. The additive and multiplicative uncertainties are combined to obtain the overall systematic uncertainties. The branching fraction systematic uncertainties include the uncertainties in the normalization mode branching fractions.
B 90% U.L. ð×10−7Þ
Decay mode Nsig(candidates) ϵsig (%) B ð×10−7Þ BABAR Previous
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